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At least 91 records · Page 5Linked to original sources
USGS1992

Interactive inversion of dipole loop-loop electromagnetic data for layered earth models using numerical integration and complex image theory (version 1.0)

This report is provided as a reference guide to define the basic graphical user interface (GUI) responses needed to perform interactive forward or inverse modeling of dipole loop-loop electromagnetic (EM) data using an IBM compatible personal computer (PC). The underlying model used is a one-dimensional (1-D) horizontal layered earth with parameters being the layer resistivities and thicknesses below the earth's surface. Mathematical details of the layered earth modeling are summarized below and in Appendix 1 that describes two general methods: numerical integration and complex image theory to compute forward or inverse sounding curves in the frequency-domain. Any combination of 5-different dipole loop-loop geometries can be selected in the modeling. The program in this report is named INVDP (for INVersion of DiPole data).

Open-File Report↗
USGS2007

Calculation of nonlinear confidence and prediction intervals for ground-water flow models

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Journal of the American Water Resources Associatio↗
USGS1989

Predicting earthquakes by analyzing accelerating precursory seismic activity

During 11 sequences of earthquakes that in retrospect can be classed as foreshocks, the accelerating rate at which seismic moment is released follows, at least in part, a simple equation. This equation (1) is {Mathematical expression},where {Mathematical expression} is the cumulative sum until time, t, of the square roots of seismic moments of individual foreshocks computed from reported magnitudes;C and n are constants; and tfis a limiting time at which the rate of seismic moment accumulation becomes infinite. The possible time of a major foreshock or main shock, tf,is found by the best fit of equation (1), or its integral, to step-like plots of {Mathematical expression} versus time using successive estimates of tfin linearized regressions until the maximum coefficient of determination, r2,is obtained. Analyzed examples include sequences preceding earthquakes at Cremasta, Greece, 2/5/66; Haicheng, China 2/4/75; Oaxaca, Mexico, 11/29/78; Petatlan, Mexico, 3/14/79; and Central Chile, 3/3/85. In 29 estimates of main-shock time, made as the sequences developed, the errors in 20 were less than one-half and in 9 less than one tenth the time remaining between the time of the last data used and the main shock. Some precursory sequences, or parts of them, yield no solution. Two sequences appear to include in their first parts the aftershocks of a previous event; plots using the integral of equation (1) show that the sequences are easily separable into aftershock and foreshock segments. Synthetic seismic sequences of shocks at equal time intervals were constructed to follow equation (1), using four values of n. In each series the resulting distributions of magnitudes closely follow the linear Gutenberg-Richter relation log N=a-bM, and the product n times b for each series is the same constant. In various forms and for decades, equation (1) has been used successfully to predict failure times of stressed metals and ceramics, landslides in soil and rock slopes, and volcanic eruptions. Results of more recent experiments and theoretical studies on crack propagation, fault mechanics, and acoustic emission can be closely reproduced by equation (1). Rate-process theory and continuum damage mechanics offer leads toward understanding the physical processes. ?? 1989 Birkha??user Verlag.

Pure and Applied Geophysics PAGEOPH↗
USGS1982

Two BASIC computer programs for the determination of in situ stresses using the CSIRO hollow inclusion stress cell and the USBM borehole deformation gage

The mathematical method of determining in-situ stresses by overcoring, using either the U.S. Bureau of Mines Borehole Deformation Gage or the Commonwealth Scientific and Industrial Research Organisation Hollow Inclusion Stress Cell, is summarized, and data reduction programs for each type of instrument, written in BASIC, are presented. The BASIC programs offer several advantages over previously available FORTRAN programs. They can be executed on a desk-top microcomputer at or near the field site, allowing the investigator to assess the quality of the data and make decisions on the need for additional testing while the crew is still in the field. Also, data input is much simpler than with currently available FORTRAN programs; either English or SI units can be used; and standard deviations of the principal stresses are computed as well as those of the geographic components.

Open-File Report↗
USGS1993

Courant number and unsteady flow computation

The Courant number C, the key to unsteady flow computation, is a ratio of physical wave velocity, ??, to computational signal-transmission velocity, ??, i.e., C = ??/??. In this way, it uniquely relates a physical quantity to a mathematical quantity. Because most unsteady open-channel flows are describable by a set of n characteristic equations along n characteristic paths, each represented by velocity ??i, i = 1,2,....,n, there exist as many as n components for the numerator of C. To develop a numerical model, a numerical integration must be made on each characteristic curve from an earlier point to a later point on the curve. Different numerical methods are available in unsteady flow computation due to the different paths along which the numerical integration is actually performed. For the denominator of C, the ?? defined as ?? = ?? 0 = ??x/??t has been customarily used; thus, the Courant number has the familiar form of C?? = ??/??0. This form will be referred to as ???common Courant number??? in this paper. The commonly used numerical criteria C?? for stability, neutral stability and instability, are imprecise or not universal in the sense that r0 does not always reflect the true maximum computational data-transmission speed of the scheme at hand, i.e., Ctau is no indication for the Courant constraint. In view of this , a new Courant number, called the ???natural Courant number???, Cn, that truly reflects the Courant constraint, has been defined. However, considering the numerous advantages inherent in the traditional C??, a useful and meaningful composite Courant number, denoted by C??* has been formulated from C??. It is hoped that the new aspects of the Courant number discussed herein afford the hydraulician a broader perspective, consistent criteria, and unified guidelines, with which to model various unsteady flows.

Conference Paper↗
USGS1953

A modification in the technique of computing average lengths from the scales of fishes

In virtually all the studies that employ scales, otollths, or bony structures to obtain the growth history of fishes, it has been the custom to compute lengths for each individual fish and from these data obtain the average growth rates for any particular group. This method involves a considerable amount of mathematical manipulation, time, and effort. Theoretically it should be possible to obtain the same information simply by averaging the scale measurements for each year of life and the length of the fish employed and computing the average lengths from these data. This method would eliminate all calculations for individual fish. Although Van Oosten (1929: 338) pointed out many years ago the validity of this method of computation, his statements apparently have been overlooked by subsequent investigators.

Progressive Fish-Culturist↗
USGS1991

An empirical coverage test for the g-sample problem

A nonparametric g-sample empirical coverage test has recently been developed for univariate continuous data. It is based upon the empirical coverages which are spacings of multiple random samples. The test is capable of detecting any distributional differences which may exist among the parent populations, without additional assumptions beyond randomness and continuity. The test can be effective with the limited and/or unequal sample sizes most often encountered in geologic studies. A computer program for implementing this procedure, G-SECT 1, is available. ?? 1991 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1970

Hydrologic effects of floodwater-retarding structures on Garza-Little Elm Reservoir, Texas

The Texas District of the Water Resources Division of the U.S. Geological Survey has collected and analyzed hydrologic data since 1953 to define the effects of systems of floodwater-retarding structures on downstream water and sediment yield. The district project includes 11 study areas ranging from 18 to 80 square miles in size and from 0 to 67 in percent of study area controlled by floodwaterretarding structures. The 11 study areas are within that part of Texas where the west-to-east average annual runoff ranges from about 2 to 7 inches. This report presents results of analyses, development of methodolgy, and results of application of methods for defining the downstream effects of systems of floodwaterretarding structures. Annual inflow to and outflow from the system of floodwater-retarding reservoirs in seven of the 11 study areas were found to be related by the equation: O=0.98/ 0.68, where O is annual outflow, in inches, and / is annual net inflow, in inches. Transmission loss of structure outflow to the downstream study-area stream-gaging station was determined and compared with the transmission loss of natural flood flow between tandem stream-gaging stations on Denton Creek, a tributary to Elm Fork Trinity River above Dallas. Trap efficiency of most floodwater-retarding structures was found by the U.S. Soil Conservation Service to be about 97 percent. Downstream increases in suspended-sediment concentration in the outflow were found to be large in a study area with mostly silt and clay sediments, but even a large increase in suspendedsediment concentration did not represent a significant quantitative pickup of sediment by the outflow water. Water consumption in floodwater-retarding reservoirs from the combined actions of evaporation, evapotranspiration, and seepage was found to be as much as twice the average annual consumption attributable to evaporation alone. Average annual consumption in reservoirs in the seven study areas analyzed ranged from 1.57 inches of equivalent runoff in the easternmost study area, where annual runoff averaged 6.96 inches, to 0.77 inch of equivalent runoff in the westernmost study area, where the average annual runoff was 2.35 inches. The effect of consumption on downstream flow is partially offset by rainfall on pool surface. Studies covering as much as 15 years of streamflow record at the stream-gaging stations that gage outflow from the Deep and Honey Creek study areas indicated no increase in base flow. Multiple-linear-regression techniques were used in developing methodology to determine reservoir consumption in seven study areas. The physical and climatic fnctors influencing consumption were grouped as variables in regard to their relative effect on the actions of evaporation, evapotranspiration, and seepage. The resulting generalized equation was then used in synthesizing the consumptive effects of a planned system of 162 floodwater-retarding reservoirs controlling 26 percent of a 1,660-square-mile drainage basin upstream from a major water-supply reservoir. The analyses were based on the assumption that all water consumed at the floodwater-retarding reservoirs would have reached the downstream watersupply reservoir. Water-sediment discharge relationships were derived for the runoff into the structures as well as for the runoff through and below the structures. A mathematical response model of the floodwater-retarding reservoir systems and the entire drainage basin was computer programed to yield monthly water and sediment inflow to the water-supply reservoir. Results of the response model showed that with full development, depletion of annual yield to the large reservoir would be as much as 10 percent in the early years; but after the permanent pools of the floodwater-retarding structures had mostly filled with sediment, depletion of annual yield would be generally less than 1 percent. The depletion of yield to Garza-Little Elm Reservoir during the 39-year synthesized period of study was estimated as 296,800 acre-feet out of 18,256,000 acre-feet total yield. During the same period, the floodwater-retarding structures were estimated to have kept 19,700 acre-feet of sediment from being deposited in the reservoir. "Firm"- or "critical"-yield studies were made of the large reservoir on the basis of two sets of conditions : with floodwater-retarding structures in the drainage basin, and without such structures. Results of the firm-yield studies indicated that with full development, annual firm yield would be initially reduced by 10 percent. After 30 or more years, when the permanent pools of the floodwaterretarding reservoirs would be mostly filled with sediment, the firm yield would be almost the same with or without the upstream development.

Texas↗
USGS1994

An experimental study of zinc chloride speciation from 300 to 600 °C and 0.5 to 2.0 kbar in buffered hydrothermal solutions

The solubility of sphalerite (ZnS) was measured in KCl-HCl-H 2 O solutions at 300–600°C and 0.5–2.0 kbar. The silicate assemblage K-feldspar-muscovite (or andalusite)-quartz was used to buffer the solution to acid conditions, resulting in the total solubility reaction 2 K + + KAl 2 AlSi 3 O 10 ( OH ) 2 + 6 SiO 2 + ZnS + nCl − = ZnCl n (2− n ) + 3 KAlSi 3 O 8 + H 2 S . (muscovite) (quartz) (sphalerite) (K-feldspar) A computer retrieval technique was used to derive average chloride ligand numbers for chlorozinc species at 0.25–2.0 molal total chloride. This technique mathematically solves for the average ligand number using a series of pertinent chemical relations at P and T . Mono- and di-chlorozinc species were found to predominate throughout the pressure-temperature-composition range investigated. The logarithms of the first and second dissociation constants for ZnCl 2 0 were evaluated over the P - T range; for example, at 1 kbar, the values −0.41 and −1.42 were computed for the logarithm of the first dissociation constant, while −7.62 and −10.57 were computed for the logarithm of the second dissociation constant, for 400 and 500°C, respectively. Results are compared to past studies conducted at subcritical conditions and differ in that we find no evidence for more highly coordinated chloro-zinc species except possibly for ZnCl 3 − at 600°C, 1 and 2 kbar. Our results are consistent with electrostatic theory, which favors lower charged to neutral molecules in low dielectric-constant media.

Geochimica et Cosmochimica Acta↗
USGS1980

Channel and dynamic flow characteristics of the Chattahoochee River, Buford Dam to Georgia Highway 141

Detailed flow and cross-section data for a 17-mile reach of the Chattahoochee River in northeast Georgia are described and summarized. Flow data include measurements of highly dynamic stage and discharge at five stations during the period March 21-23, 1976. Flow data were collected at 5-minute intervals and are listed accordingly. Coordinate data for 39 cross sections in the study reach are also listed. A mathematical model is developed and applied whereby stage data collected at a single station can be used to compute highly dynamic discharge at the station. The model is based on the continuity and momentum equations that describe unsteady, one-dimensional flow in open channels. Both equations are transformed to a single quadratic equation which describes mean flow velocity at a single station. Flow-geometry parameters used by the model are computed using cross-section coordinates and the equation which describes the area of an irregular polygon. Use of the model in conjunction with highly dynamic stage data collected on March 23, 1976, provided close agreement between measured and computed discharges. The model was also used to investigate the sensitivity of highly dynamic discharge to channel and flow parameters. Computed discharge was most sensitive to changes in channel roughness and slope.

Georgia↗
USGS1977

A computer program to calculate the resistivity and induced polarization response for a three-dimensional body in the presence of buried electrodes

Three-dimensional induced polarization and resistivity modeling for buried electrode configurations can be achieved by adapting surface integral techniques for surface electrode configurations to buried electrodes. Modification of. the surface technique is accomplished by considering the additional mathematical terms required to express-the changes in the electrical potential and geometry caused by placing the source and receiver electrodes below the surface. This report presents a listing of a computer program to calculate the resistivity and induced polarization response from a three-dimensional body for buried electrode configurations. The program is designed to calculate the response for the following electrode configurations: (1) hole-to-surface array with a buried bipole source and a surface bipole receiver, (2) hole-to-surface array with a buried pole source and a surface bipole receiver, (3) hole-to-hole array with a buried, fixed pole source and a moving bipole receiver, (4) surface-to-hole array with a fixed pole source on the surface and a moving bipole receiver in the borehole, (5) hole-to-hole array with a buried, fixed bipole source and a buried, moving bipole receiver, (6) hole-to-hole array with a buried, moving bipole source and a buried, moving bipole receiver, and (7) single-hole, buried bipole-bipole array. Input and output examples are given for each of the arrays.

Open-File Report↗
USGS2001

Attractor reconstruction for non-linear systems: a methodological note

Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.

Mathematical Biosciences↗
USGS2004

Extracting transient Rayleigh wave and its application in detecting quality of highway roadbed

This paper first explains the tau-p mapping method of extracting Rayleigh waves (LR waves) from field shot gathers. It also explains a mathematical model of physical character parameters of quality of high-grade roads. This paper then discusses an algorithm of computing dispersion curves using adjacent channels. Shear velocity and physical character parameters are obtained by inversion of dispersion curves. The algorithm using adjacent channels to calculating dispersion curves eliminates average effects that exist by using multi-channels to obtain dispersion curves so that it improves longitudinal and transverse resolution of LR waves and precision of non-invasive detection, and also broadens its application fields. By analysis of modeling results of detached computation of the ground roll and real examples of detecting density and pressure strength of a high-grade roadbed, and by comparison of shallow seismic image method with borehole cores, we concluded that: 1 the abnormal scale and configuration obtained by LR waves are mostly the same as the result of shallow seismic image method; 2 an average relative error of density obtained from LR waves inversion is 1.6% comparing with borehole coring; 3 transient LR waves in detecting density and pressure strength of a high-grade roadbed is feasible and effective.

Conference Paper↗
USGS1989

A general method for generating bathymetric data for hydrodynamic computer models

To generate water depth data from randomly distributed bathymetric data for numerical hydrodymamic models, raw input data from field surveys, water depth data digitized from nautical charts, or a combination of the two are sorted to given an ordered data set on which a search algorithm is used to isolate data for interpolation. Water depths at locations required by hydrodynamic models are interpolated from the bathymetric data base using linear or cubic shape functions used in the finite-element method. The bathymetric database organization and preprocessing, the search algorithm used in finding the bounding points for interpolation, the mathematics of the interpolation formulae, and the features of the automatic generation of water depths at hydrodynamic model grid points are included in the analysis. This report includes documentation of two computer programs which are used to: (1) organize the input bathymetric data; and (2) to interpolate depths for hydrodynamic models. An example of computer program operation is drawn from a realistic application to the San Francisco Bay estuarine system. (Author 's abstract)

Open-File Report↗
USGS1996

A three-dimensional method-of-characteristics solute-transport model (MOC3D)

This report presents a model, MOC3D, that simulates three-dimensional solute transport in flowing ground water. The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay). The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation. MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step. This implementation of the method of characteristics uses particle tracking to represent advective transport and explicit finite-difference methods to calculate the effects of other processes. However, the explicit procedure has several stability criteria that may limit the size of time increments for solving the transport equation; these are automatically determined by the program. For improved efficiency, the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation. However, the transport subgrid must have uniform grid spacing along rows and columns. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model was evaluated for several problems for which exact analytical solutions are available and by benchmarking against other numerical codes for selected complex problems for which no exact solutions are available. These test results indicate that the model is very accurate for a wide range of conditions and yields minimal numerical dispersion for advection-dominated problems. Mass-balance errors are generally less than 10 percent, and tend to decrease and stabilize with time.

Water-Resources Investigations Report↗
USGS1988

Experiments with microcomputer-based artificial intelligence environments

The U.S. Geological Survey (USGS) has been experimenting with the use of relatively inexpensive microcomputers as artificial intelligence (AI) development environments. Several AI languages are available that perform fairly well on desk-top personal computers, as are low-to-medium cost expert system packages. Although performance of these systems is respectable, their speed and capacity limitations are questionable for serious earth science applications foreseen by the USGS. The most capable artificial intelligence applications currently are concentrated on what is known as the "artificial intelligence computer," and include Xerox D-series, Tektronix 4400 series, Symbolics 3600, VAX, LMI, and Texas Instruments Explorer. The artificial intelligence computer runs expert system shells and Lisp, Prolog, and Smalltalk programming languages. However, these AI environments are expensive. Recently, inexpensive 32-bit hardware has become available for the IBM/AT microcomputer. USGS has acquired and recently completed Beta-testing of the Gold Hill Systems 80386 Hummingboard, which runs Common Lisp on an IBM/AT microcomputer. Hummingboard appears to have the potential to overcome many of the speed/capacity limitations observed with AI-applications on standard personal computers. USGS is a Beta-test site for the Gold Hill Systems GoldWorks expert system. GoldWorks combines some high-end expert system shell capabilities in a medium-cost package. This shell is developed in Common Lisp, runs on the 80386 Hummingboard, and provides some expert system features formerly available only on AI-computers including frame and rule-based reasoning, on-line tutorial, multiple inheritance, and object-programming. ?? 1988 International Association for Mathematical Geology.

Mathematical Geology↗
USGS1987

On the functional optimization of a certain class of nonstationary spatial functions

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail. ?? 1987 Plenum Publishing Corporation.

Journal of Optimization Theory and Applications↗